An attempt to solve a problem appearing in physics by formulation and numerical computation often ends up solving simultaneous linear equations. The LINPACK benchmark is known as a benchmark for measuring the computational performance of a computer system for solving simultaneous linear equations as above. Since the LINPACK benchmark is used for the ranking on the TOP500 list, attention has been drawn to a technique to solve simultaneous linear equations using a computer system at high speed. Here, LINPACK itself is a software library for performing numerical computations. Particularly, high-performance LINPACK (HPL) is a library for nodes (for example, processes or processor cores) of a parallel computer system to solve simultaneous linear equations for a dense matrix in parallel.
In the computation of simultaneous linear equations Ax=b, the matrix A is first factorized into an upper triangular matrix and a lower triangular matrix (this factorization is called the LU factorization), and then x is obtained. For this reason, if shortening of the processing time of LU-factorization is achieved, it is possible to shorten the time taken to solve simultaneous linear equations. An example of the related conventional technique is disclosed in, for example, Japanese Laid-open Patent Publication No. 07-271760.
In one aspect, an object of the present disclosure is to provide a technique for shortening processing time of LU-factorization by a parallel computer.